D. Michael Ray

Articles

Canonical correlation in geographical analysis

D. Michael Ray, Paul R. Lohnes

Geographia Polonica (1973) vol. 25, pp. 49-67 | Full text

Further information

Abstract:

It is the purpose of this paper to describe and illustrate a number of interpretivedevices which have recently emerged and which have not before beenutilized in the geographic literature. These devices are the computation of thecanonical factor structure matrix, the variances extracted from each measurementdomain by the canonical factors, the redundancy of the canonical factorsof one set given those of the other, and the canonical factor scores. The canonicalfactor structure matrix provides the correlations of the variables (or measurementdomain) with the canonical factors and takes the place of the raw canonicalvectors in which the variances are uncontrolled. The variances extractedfrom a measurement domain by a canonical factor may shrink to insignificanceif its canonical correlation with the corresponding factor for the othermeasurement domain is low. A better measure of the interrelationships betweenthe two measurement domains being analyzed is the redundancy measure,which is the product of the variance extracted and the variance shared foreach pair of canonical factors. This paper also introduces the notion of canonicalfactor scores which correspond to the scores computed in principal componentsanalysis and which provide a mapping of the observation units into thecanonical factor space. The computation of these indexes is described in the mathematicalsection which follows. Two research examples are then providedto illustrate the application and interpretation of the technique.

D. Michael Ray, State University of New York, Buffalo
Paul R. Lohnes, State University of New York, Buffalo

Urban Growth and the Concept of Functional Region

D. Michael Ray

Geographia Polonica (1968) vol. 15, pp. 199-246 | Full text

Further information

Abstract:

Urban growth is dependent upon the number and types of goods and services provided for functional regions and is related to the size and population of the functional regions served. The usual cliche is that cities do not thrive where people merely take in one another's washing. "Cities do not grow up of themselves. Countrysides set them up to do tasks that must be performed in central place" 1. The tasks set reflect geogra-phic location. There is, therefore, a sequential relationship between geographic location, urban functions, functional regions and urban growth. The form of the sequential relationship is traced in this biblio-graphic essay by examining the nature and type of urban functions and functional regions, and by reviewing the contribution of location theories to understanding the size and spacing of urban functions and urban places. The relationship is then illustrated by focusing attention on one area, Eastern Ontario, where urban growth has been retarded by the slow expansion of manufacturing industry and is dependent largely upon the central-place functions performed.

D. Michael Ray, State University of New York, Buffalo